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Geometrical aspects of the Landau-Hall problem on the hiperbolic plane.

A. López Almorox;  C. Tejero Prieto — 2001

RACSAM

Se discuten algunos aspectos del problema de Landau-Hall hiperbólico. El álgebra de Lie de las simetrías infinitesimales de este problema se da explícitamente, resultando ser isomorfa a so(2,1) y que sus invariantes Noether asociados son los momentos angulares hiperbólicos. Asimismo se desarrolla la formulación hamiltoniana, lo que nos permitirá obtener la variedad de órbitas de energía constante de este problema mediante técnicas de reducción simpléctica.

Natural operations on holomorphic forms

A. Navarro;  J. Navarro;  C. Tejero Prieto — 2018

Archivum Mathematicum

We prove that the only natural differential operations between holomorphic forms on a complex manifold are those obtained using linear combinations, the exterior product and the exterior differential. In order to accomplish this task we first develop the basics of the theory of natural holomorphic bundles over a fixed manifold, making explicit its Galoisian structure by proving a categorical equivalence à la Galois.

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